Shack-Hartmann wavefront sensor optical dynamic range

Learning-based lens wavefront aberration recovery

Wavefront aberration describes the deviation of a wavefront in an imaging system from a desired perfect shape, such as a plane or a sphere, which may be caused by a variety of factors, such as imperfections in optical equipment, atmospheric turbulence, and the physical properties of imaging subjects and medium. Measuring the wavefront aberration of an imaging system is a crucial part of modern optics and optical engineering, with a variety of applications such as adaptive optics, optical testing, microscopy, laser system design, and ophthalmology. While there are dedicated wavefront sensors that aim to measure the phase of light, they often exhibit some drawbacks, such as higher cost and limited spatial resolution compared to regular intensity measurement. In this paper, we introduce a lightweight and practical learning-based method, named LWNet, to recover the wavefront aberration for an imaging system from a single intensity measurement. Specifically, LWNet takes a measured point spread function (PSF) as input and recovers the wavefront aberration with a two-stage network. The first stage network estimates an initial wavefront aberration via supervised learning, and the second stage network further optimizes the wavefront aberration via self-supervised learning by enforcing the statistical priors and physical constraints of wavefront aberrations via Zernike decomposition. For supervised learning, we created a synthetic PSF-wavefront aberration dataset via ray tracing of 88 lenses. Experimental results show that even trained with simulated data, LWNet works well for wavefront aberration estimation of real imaging systems and consistently outperforms prior learning-based methods.

Large Range of a High-Precision, Independent, Sub-Mirror Three-Dimensional Co-Phase Error Sensing and Correction Method via a Mask and Population Algorithm

The emergence of segmented mirrors is expected to solve the design, processing, manufacturing, testing, and launching of space telescopes of large apertures. However, with the increase in the number of sub-mirrors, the sensing and correction of co-phase errors in segmented mirrors will be very difficult. In this paper, an independent three-dimensional method for sub-mirror co-phase error sensing and correction method is proposed. The method is based on a wide spectral modulation transfer function (MTF), mask, population optimization algorithm, and online model-free correction. In this method, the sensing and correction process of each sub-mirror co-phase error is independent of each other, so the increase in the number of sub-mirrors will not increase the difficulty of the method. This method can sense and correct the co-phase errors of three dimensions of the sub-mirror, including piston, tip, and tilt, even without modeling the optical system, and has a wide detection range and high precision. And the efficiency is high because the sub-mirrors can be corrected simultaneously in parallel. Simulation results show that the proposed method can effectively sense and correct the co-phase errors of the sub-mirrors in the range [-50λ, 50λ] in three dimensions with high precision. The average RMSE value in 100 experiments of the true co-phase error values and the experimental co-phase error values of one of the six sub-mirrors is 2.358 × 10-7λ.

Method for testing freeform surfaces based on a Shack-Hartmann sensor with plane wavefront scanning and stitching

Currently, the surface error measurement technology for freeform faces a significant contradiction between measurement accuracy and dynamic range. The study proposes a non-null testing method for measuring freeform surfaces by utilizing a Shack-Hartmann wavefront sensor to emit a small aperture parallel beam and scan along the normal direction at the center of subapertures for stitching (SHPSS). A mathematical model based on ray tracing and the reflection theorem is established to calculate the sampling points on an ideal freeform surface, the reference spot array on CCD, and the corresponding relationship between microlens array and spots. An algorithm is proposed to iteratively calculate the wavefront aberration and gradually approach the actual sampling points using the established model. Theoretical analysis and numerical simulation results indicate that SHPSS can increase the dynamic range and improve the accuracy of wavefront reconstruction. The error analysis of the SHPSS method is carried out, the measurement accuracy of full aperture freeform surface is 11.45 nm. A testing system is set up and experiments are conducted on a 100 mm aperture freeform reflective mirror. The RMS of the SHPSS test results is less than λ/30 (λ=635 nm) compared to the interferometric test results. By analyzing five groups of repeated measurement experiments, the repeatability accuracy of SHPSS method is less than 1/80 λ (RMS). This demonstrates the feasibility and measurement capabilities of the method for freeform surface testing.

Advanced Optical Wavefront Technologies to Improve Patient Quality of Vision and Meet Clinical Requests

Adaptive optics (AO) is employed for the continuous measurement and correction of ocular aberrations. Human eye refractive errors (lower-order aberrations such as myopia and astigmatism) are corrected with contact lenses and excimer laser surgery. Under twilight vision conditions, when the pupil of the human eye dilates to 5-7 mm in diameter, higher-order aberrations affect the visual acuity. The combined use of wavefront (WF) technology and AO systems allows the pre-operative evaluation of refractive surgical procedures to compensate for the higher-order optical aberrations of the human eye, guiding the surgeon in choosing the procedure parameters. Here, we report a brief history of AO, starting from the description of the Shack-Hartmann method, which allowed the first in vivo measurement of the eye's wave aberration, the wavefront sensing technologies (WSTs), and their principles. Then, the limitations of the ocular wavefront ascribed to the IOL polymeric materials and design, as well as future perspectives on improving patient vision quality and meeting clinical requests, are described.

Robust and accurate measurement of optical freeform surfaces with wavefront deformation correction

The non-null test to detect the modulated wavefront is a widely used method in optical freeform surface measurement. In this study, the wavefront deformation in the non-null test of an optical freeform surface measurement was corrected based on the wavefront propagation model to improve measurement accuracy. A freeform surface wavefront correction (FSWC) measurement system was established to validate the proposed method. Simulation and experimental studies indicated that the proposed method can reduce the influence of freeform surface wavefront deformation in space propagation. Moreover, the freeform surface form accuracy measured by FSWC can reach a root-mean-squared value of 10 nm.

Computational Method for Wavefront Sensing Based on Transport-of-Intensity Equation

Recently the transport-of-intensity equation as a phase imaging method turned out as an effective microscopy method that does not require the use of high-resolution optical systems and a priori information about the object. In this paper we propose a mathematical model that adapts the transport-of-intensity equation for the purpose of wavefront sensing of the given light wave. The analysis of the influence of the longitudinal displacement z and the step between intensity distributions measurements on the error in determining the wavefront radius of curvature of a spherical wave is carried out. The proposed method is compared with the traditional Shack–Hartmann method and the method based on computer-generated Fourier holograms. Numerical simulation showed that the proposed method allows measurement of the wavefront radius of curvature with radius of 40 mm and with accuracy of ~200 μm.